82.54.5 problem Ex. 5

Internal problem ID [18950]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 5
Date solved : Monday, March 31, 2025 at 06:26:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=(x-3)*diff(diff(y(x),x),x)-(4*x-9)*diff(y(x),x)+3*(x-2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 +c_2 \left (4 x^{3}-42 x^{2}+150 x -183\right ) {\mathrm e}^{2 x}\right ) \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 42

ode=(x-3)*D[y[x],{x,2}]-(4*x-9)*D[y[x],x]+3*(x-2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} c_2 e^{3 x-9} \left (4 x^3-42 x^2+150 x-183\right )+c_1 e^{x-3} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 3)*Derivative(y(x), (x, 2)) + (3*x - 6)*y(x) - (4*x - 9)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False